AITA for not letting a family friend see her cat?

TLDR; I won’t let my family friend visit her cat because the cat hasn’t gotten used to her new environment yet. The cat is also staying at my grandma’s house, who doesn’t know this friend and doesn’t want strangers roaming around her house.

I (29f) have a family friend (61f) that had adopted a cat from my boyfriend’s (33m) family several years ago. I will refer to the family friend as Mary.

Mary had an apartment when she first adopted the cat, and she chose to move several states away to live with family, giving up her very cheap apartment. She took the cat with her.

My boyfriend got a call from her last week, saying she was getting on a flight back to our state with the cat because she was abruptly kicked out of her family’s home in Florida. She flew back here and she is now homeless.

We really felt terrible about the cat being so old (she’s 14) and potentially having to go to a shelter, so I asked my grandmother (80f) if she’d be willing to house the cat temporarily till Mary gets on her feet. She agreed, which was very generous of her considering she does not know Mary. In fact, I barely know her myself.

I brought the cat to my grandmothers house 5 days ago. The cat is still very skittish in her new environment and has been hiding out in the basement. But she’s eating, drinking, using the litter box, and slowly getting acclimated to her surroundings.

Mary has been contacting me multiple times per day for the past couple days, begging to come see the cat. It has gotten to the point where she wants my grandmothers number so she can start calling her directly.

We’ve told Mary that as soon as the cat is comfortable, we will start sending her pictures and discuss arranging a visit. We are not keeping the cat from her at all, but we are prioritizing lessening the anxiety of an innocent animal that just moved to a new home, lost her owner, and endured a 14 hour flight.

My grandmother isn’t comfortable with a stranger poking around her basement looking for a cat that’s still in hiding, and I think it’s unfair to the cat to have her owner show up randomly making her think she’s going home, just for the owner to disappear again. It just seems cruel to me.

Mary is becoming increasingly persistent and it’s making me uncomfortable. AITA for not allowing her to see the cat yet?